Statistical Sciences

The course is structured into four parts focused on theoretical aspects and applications. Part 1: Introduction and theoretical background (about 17%). Introduction to relational data between objects (statistical units and variables). Two-Way e Three-Way Data. Fundamentals of matrix algebra. Symmetric and asymmetric data matrices: proximity measures between statistical units and variables. Part 2: Dimensionality reduction methods for matrices of relationships between variables (about 50%). Models, analytical details, properties and applications: Principal Component Analysis Canonical Correlation Analysis Redundancy Analysis and Regression Part 3: Dimensionality reduction methods for symmetric relational data between units (about 17%) Two-Way Data: Metric and Non-Metric MDS Three-Way Data: INDSCAL, INDCLUS Part 4: Dimensionality reduction methods for asymmetric relational data (about 12%) MDS and Cluster Analysis Individual presentations on in-depth topics (4%) Real data using Matlab and/or SAS will be analyzed with a special focus on the interpretation of the output concerning the methodologies learned in the theoretical part.

To successfully acquire the necessary skills and pass the exam, students are required to know the fundamentals of Statistics, specifically the basic concepts of descriptive statistics and Inference, as well as the classical methodologies of Multivariate Statistics. These are required courses in the degree program. Additionally, students are recommended to know some basic notion of matrix algebra.

Everitt, B. S., Rabe-Hesketh, S., The Analysis of Proximity Data, Arnold, London, 1997. K.V. Mardia, J.T. Kent, J.M. Bibby, Multivariate Analysis, Academic Press, 1994. Jos M.F. ten Berge, Least Squares Optimization in Multivariate Analysis, DSWO Press, Leiden, 2005. Teacher's notes and scripts

Lectures in presence (up to health emergency) are focused on both theoretical and practical aspects of the advanced methodologies for the analysis of relational data. The coursework in the Computer Lab alternates lectures and applications to real case studies to link theory and practice in a self-directed learning.

Attendance in this course is strongly recommended. In case of impossibility, students are encouraged to contact the teacher.

To pass the exam the student needs to pass a final oral exam to test the knowledge of the theoretical concepts. During the semester students may carry out a series of assignments that include some analyses of real case-studies and produce a (short) technical report. Such an assessment allows to assess both the knowledge of the theoretical concepts and the capability to formalize the statistical goal plus the ability to build a strategy of analysis to solve practical problems.

Rencher, A. C., Methods of Multivariate Analysis ,Wiley, 2002. SAITO, T., and YADOHISA, H., Data Analysis of Asymmetric Structures. Advanced Approaches in Computational Statistics, New York: Marcel Dekker, 2005. Jos M.F. ten Berge, Least Squares Optimization in Multivariate Analysis, DSWO Press, Leiden, 2005. BOVE, G., OKADA, A., VICARI, D., Methods for the Analysis of Asymmetric Relationships, Series: Behaviormetrics: Quantitative Approaches to Human Behavior, Springer Nature, Singapore, 2021.

Lectures in presence are focused on both theoretical and practical aspects of the advanced methodologies for the analysis of relational data. The coursework in the Computer Lab alternates lectures and applications to real case studies to link theory and practice in a self-directed learning.